Some have used Zernike polynomials to calculate wavefront measurements of refraction aberrations of an eye and have used second order terms of the Zernike polynomial expansion for defining the aberration wavefront from which the refractive be used to derive spherical correction and orthogonal and oblique astigmatism terms can be used to derive cylinder and axis correction. Subjective eye examinations typically use a device such as a phoropter to provide a patient with choices among proposed sphero-cylindrical corrections. Different lenses with stepwise varied magnification spherical magnification and cylindrical magnification are alternately placed in the field of vision and the patient is asked to subjectively select which one provides the best vision. The cylindrical lenses are rotated to determine the angular orientation of the astigmatism. Corrective prescriptions are typically provided in terms of spherical correction (+/−diopter) and cylindrical correction (+/−diopter at an angle) for providing vision corrections such as external spectacle lenses, contact lenses, implanted lenses, corneal ablation with Eximer laser surgery (laser vision correction).
Objective measurements of refraction of the eye have been accomplished using various technologies. Modern objective measurement technology makes measurements from which wavefront aberrations are determined and expressed in terms of mathematical functions useful for approximating the shape or slope of the wavefront contrasted to a wave front that would be produced by an eye with theoretically perfect refraction. Curve fitting using Zernike polynomial expansion has become one standard for mathematically expressing an approximation for the refraction aberration wavefront. From the approximation thus determined, correction to the vision is mostly produced according to sphero-cylindrical corrections. Or as is recently possible with custom laser vision correction.